core/spire.math/Jet

Jet

@SerialVersionUID(0L) final case
class Jet[@specialized(Float, Double) T](real: T, infinitesimal: Array[T]) extends ScalaNumber with ScalaNumericConversions with Serializable
Companion
object
trait Product
trait Equals
trait ScalaNumericConversions
trait ScalaNumericAnyConversions
class ScalaNumber
class Number
trait Serializable
class Object
trait Matchable
class Any
Jet[T]

Value members

Concrete methods

def %(b: Jet[T])(implicit c: ClassTag[T], f: Field[T], r: IsReal[T], v: VectorSpace[Array[T], T]): Jet[T]
def *(b: T)(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def *(b: Jet[T])(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def **(b: Int)(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def **(b: Jet[T])(implicit c: ClassTag[T], f: Field[T], s: Signed[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]
def +(b: T)(implicit f: Field[T]): Jet[T]
def +(b: Jet[T])(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def -(b: T)(implicit f: Field[T]): Jet[T]
def -(b: Jet[T])(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def /(b: T)(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def /(b: Jet[T])(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def /%(b: Jet[T])(implicit c: ClassTag[T], f: Field[T], r: IsReal[T], v: VectorSpace[Array[T], T]): (Jet[T], Jet[T])
def /~(b: Jet[T])(implicit c: ClassTag[T], f: Field[T], r: IsReal[T], v: VectorSpace[Array[T], T]): Jet[T]
def =!=(that: Jet[_]): Boolean
def ===(that: Jet[_]): Boolean
def abs(implicit f: Field[T], s: Signed[T], v: VectorSpace[Array[T], T]): Jet[T]

abs(x + du) ~= x + du or -(x + du)

abs(x + du) ~= x + du or -(x + du)

def acos(implicit f: Field[T], n: NRoot[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

acos(a + du) ~= acos(a) - 1 / sqrt(1 - a**2) du

acos(a + du) ~= acos(a) - 1 / sqrt(1 - a**2) du

def asTuple: (T, Array[T])
def asin(implicit f: Field[T], n: NRoot[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

asin(a + du) ~= asin(a) - 1 / sqrt(1 - a**2) du

asin(a + du) ~= asin(a) - 1 / sqrt(1 - a**2) du

def atan(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

atan(a + du) ~= atan(a) + 1 / (1 + a**2) du

atan(a + du) ~= atan(a) + 1 / (1 + a**2) du

def atan2(a: Jet[T])(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

Defined with "this" as the y coordinate:

Defined with "this" as the y coordinate:

this.atan2(a) == atan2(this, a) == atan(this / a) atan2(b + dv, a + du) ~= atan2(b, a) + (- b du + a dv) / (a^2 + b^2)
override
def byteValue: Byte
Definition Classes
ScalaNumericAnyConversions -> Number
def ceil(implicit c: ClassTag[T], r: IsReal[T]): Jet[T]
def cos(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

cos(a + du) ~= cos(a) - sin(a) du

cos(a + du) ~= cos(a) - sin(a) du

def cosh(implicit t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

cosh(a + du) ~= cosh(a) + sinh(a) du

cosh(a + du) ~= cosh(a) + sinh(a) du

def dimension: Int
override
def doubleValue: Double
Definition Classes
ScalaNumericAnyConversions -> Number
override
def equals(that: Any): Boolean
Definition Classes
Equals -> Any
def eqv(b: Jet[T])(implicit o: Eq[T]): Boolean
def exp(implicit t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

exp(a + du) ~= exp(a) + exp(a) du

exp(a + du) ~= exp(a) + exp(a) du

override
def floatValue: Float
Definition Classes
ScalaNumericAnyConversions -> Number
def floor(implicit c: ClassTag[T], r: IsReal[T]): Jet[T]
override
def hashCode: Int
Definition Classes
Any
override
def intValue: Int
Definition Classes
ScalaNumericAnyConversions -> Number
def isInfinitesimal: Boolean
def isReal: Boolean
override
def isValidInt: Boolean
Definition Classes
ScalaNumericAnyConversions
override
def isWhole: Boolean
Definition Classes
ScalaNumericAnyConversions -> ScalaNumber
def isZero: Boolean
def log(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

log(a + du) ~= log(a) + du / a

log(a + du) ~= log(a) + du / a

override
def longValue: Long
Definition Classes
ScalaNumericAnyConversions -> Number
def neqv(b: Jet[T])(implicit o: Eq[T]): Boolean
def nroot(k: Int)(implicit f: Field[T], s: Signed[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]
def pow(p: T)(implicit f: Field[T], s: Signed[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

pow -- base (this) is a differentiable function, exponent is a constant.

pow -- base (this) is a differentiable function, exponent is a constant.

pow(a + du, p) ~= pow(a, p) + p * pow(a, p-1) du
def pow(p: Int)(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
def pow(b: Jet[T])(implicit c: ClassTag[T], f: Field[T], m: CModule[Array[T], T], s: Signed[T], t: Trig[T]): Jet[T]

pow -- both base (this) and exponent are differentiable functions.

pow -- both base (this) and exponent are differentiable functions.

(a + du)^(b + dv) ~= a^b + b * a^(b-1) du + a^b log(a) dv
def powScalarToJet(a: T)(implicit c: ClassTag[T], f: Field[T], m: CModule[Array[T], T], s: Signed[T], t: Trig[T]): Jet[T]
def round(implicit c: ClassTag[T], r: IsReal[T]): Jet[T]
override
def shortValue: Short
Definition Classes
ScalaNumericAnyConversions -> Number
def signum(implicit r: Signed[T]): Int

This is consistent with abs

This is consistent with abs

def sin(implicit t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

sin(a + du) ~= sin(a) + cos(a) du

sin(a + du) ~= sin(a) + cos(a) du

def sinh(implicit t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

sinh(a + du) ~= sinh(a) + cosh(a) du

sinh(a + du) ~= sinh(a) + cosh(a) du

def sqrt(implicit f: Field[T], n: NRoot[T], v: VectorSpace[Array[T], T]): Jet[T]

sqrt(a + du) ~= sqrt(a) + du / (2 sqrt(a))

sqrt(a + du) ~= sqrt(a) + du / (2 sqrt(a))

def tan(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

tan(a + du) ~= tan(a) + (1 + tan(a)**2) du

tan(a + du) ~= tan(a) + (1 + tan(a)**2) du

def tanh(implicit f: Field[T], t: Trig[T], v: VectorSpace[Array[T], T]): Jet[T]

tanh(a + du) ~= tanh(a) + (1 - tanh(a)**2) du

tanh(a + du) ~= tanh(a) + (1 - tanh(a)**2) du

override
def toString: String
Definition Classes
Any
def unary_-(implicit f: Field[T], v: VectorSpace[Array[T], T]): Jet[T]
override
def underlying: Object
Definition Classes
ScalaNumericConversions -> ScalaNumber

Inherited methods

def isValidByte: Boolean
Inherited from
ScalaNumericAnyConversions
def isValidChar: Boolean
Inherited from
ScalaNumericAnyConversions
def isValidShort: Boolean
Inherited from
ScalaNumericAnyConversions
def productElementNames: Iterator[String]
Inherited from
Product
def productIterator: Iterator[Any]
Inherited from
Product
def toByte: Byte
Inherited from
ScalaNumericAnyConversions
def toChar: Char
Inherited from
ScalaNumericAnyConversions
def toDouble: Double
Inherited from
ScalaNumericAnyConversions
def toFloat: Float
Inherited from
ScalaNumericAnyConversions
def toInt: Int
Inherited from
ScalaNumericAnyConversions
def toLong: Long
Inherited from
ScalaNumericAnyConversions
def toShort: Short
Inherited from
ScalaNumericAnyConversions
protected
def unifiedPrimitiveEquals(x: Any): Boolean
Inherited from
ScalaNumericAnyConversions
protected
def unifiedPrimitiveHashcode: Int
Inherited from
ScalaNumericAnyConversions

Implicits

Implicits

implicit
def jetDimension: JetDim